Solve the following 1 do +- PDE: dr'r dr',2 20? BCs: v, dr at r=a v, =U„ cos 0 at r= 00 1 дф Ve = = -U sin 0 r d0

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A: The given integral is I=∫01cosx2+3dx To approximate the integral using Simpson's rule.

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Q: In right AXYZ with hypotenuse XZ if cos X = and XZ 10 24. then to %3D the nearest integer XY = ?

A: Given: ∆xyz is the right angle triangle with hypotenuse xz x=710 & xz=24

Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

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A: Use trigonometric substitution method for solving the integral.

Q: 5. Find if y = sin(vT +1). dr %3D

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Q: S cos“C)dy

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Q: Use Superposition approach to find the genral solution of the following equation: y" – 2y' + 3y = -6…

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Q: 8 Find L-- 8s2+6 sin Vt cos Vt COS V V등 sin y응t COS

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Q: Find the length of the path over the given interval. (2 cost − cos 2t, 2 sin t − sin 2t), 0 ≤ t ≤…

A: x(t)=2 cost − cos 2t y(t)= 2 sin t − sin 2t interval- 0 ≤ t ≤ π/2

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A: Partially Differentiate with respect to y

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Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: The integral (cos(3x)) sin(3x)dx under the change of variable u = cos3r becomes u du. Select one: a.…

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A: Given  The integration is I=∫0π2sin3x cos3x  dx.

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Q: Find 19. t sin 3t dt Jo

A: Topic:- integration  Note:- as per our guideline if more than one question uploaded than only first…

Q: Q2- Show that, 2 sin x |Jo(x cos 0) cos 0 d0

A: We have to prove sinxx=∫0π2J0(xcosθ)cosθdθ                     (1) Since we know…

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: Ni cos(2?)a. Cos | x dx

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Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

A: We have to use derivative definition.

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

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Q: at æ = 0 for 12 sin(t)dt.

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Q: If S sin 2y cos 2y dy = =, then x is equal to: %3D

A: Hint:    sin2θ=2sinθcosθ

Q: Find the general solution of the differantial equation given by www |y" – 4y' + 5y = 3xe* – cos2x +…

A: Given y''-4y'+5y=3xex-cos2x+x+1sin2x

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Q: COS 10T - i sin 10TT 3 3 GT+ 3 of 學 4T COS 27 + 40 3 C1) - 1 2

A: Use trigonometric ratios

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Q: Which of the following is equal to s v² cos (v³)dv ? A sin 1 8 jsin 1 O Option 1 Option 2 D. sin C.…

A: The solution is Option B 13sin(1)

Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

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Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. @ y(x)…

A: We find the general solution of given DE  y"+y'=-cos(x)........(1)

Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x)…

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Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

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A: this is false because

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Q: Find the common elrea between Y=2CI+Cose) and carved V=Z(1-Sine) which is Losatel in the funrth…

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Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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